Related papers: Atomic operators in vector lattices
Using ideas of Olson \cite{Ols} who showed that the system of effect operators of a Hilbert space can be ordered by the so-called spectral order such that the system of effect operators is a complete lattice. Using his ideas, we introduce a…
Given a complete atomic Boolean algebra, we show there is a commutative BCK-algebra whose ideal lattice is that Boolean algebra. This result is shown to exist within a larger framework involving BCK-algebras of functions, whose ideals and…
The canonical operator $\hat{a}^{\dagger}$ ($\hat{a}$) represents the ideal process of adding (subtracting) an {\it exact} amount of energy $E$ to (from) a physical system in both elementary quantum mechanics and quantum field theory. This…
Let V be a vertex operator algebra and g an automorphism of order T. We construct a sequence of associative algebras A_{g,n}(V) with n\in\frac{1}{T}\Z nonnegative such that A_{g,n}(V) is a quotient of A_{g,n+1/T}(V) and a pair of functors…
We represent vector bundles over a regular algebraic curve as pairs of lattices over the maximal orders of its function field and we give polynomial time algorithms for several tasks: computing determinants of vector bundles, kernels and…
In this article we investigate the disjointly non-singular (DNS) operators. Following [8] we say that an operator $T$ from a Banach lattice $F$ into a Banach space $E$ is DNS, if no restriction of $T$ to a subspace generated by a disjoint…
A linear Lie rack structure on a finite dimensional vector space $V$ is a Lie rack operation $(x,y)\mapsto x\rhd y$ pointed at the origin and such that for any $x$, the left translation $\mathrm{L}_x:y\mapsto \mathrm{L}_x(y)= x\rhd y$ is…
In this paper we introduce the notion of an operator category and two different models for homotopy theory of $\infty$-operads over an operator category -- one of which extends Lurie's theory of $\infty$-operads, the other of which is…
We introduce and study a new class of higher order differential operators defined on $\mathbb{R}^{n}$, which are built with H\"{o}rmander vector fields, homogeneous w.r.t. a family of dilations (but not left invariant w.r.t. any structure…
This article contains the results of two types. First we give a complete characterization of band preserving projection operators on Dedekind complete vector lattices. This is done in Theorem~3.4. Let us mention also Theorem~3.2 that…
Let ${\cal S}(\mathcal{H})$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $\mathcal{H}$, which is the set of all physical quantities on a quantum system $\mathcal{H}$. We introduce a binary…
Led by the key example of the Korteweg-de Vries equation, we study pairs of Hamiltonian operators which are non-homogeneous and are given by the sum of a first-order operator and an ultralocal structure. We present a complete classification…
In this work we study a linear operator $f$ on a pre-euclidean space $\mathcal{V}$ by using properties of a corresponding graph. Given a basis $\B$ of $\mathcal{V}$, we present a decomposition of $\mathcal{V}$ as an orthogonal direct sum of…
We consider $\mathbb{R}^3$ as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary $\tau\in \widehat{SO(3)}$, let $E_\tau$ be the homogeneous vector bundle over $\mathbb{R}^3$…
The concept of determinant for a linear operator in an infinite-dimensional space is addressed, by using the derivative of the operator's zeta-function (following Ray and Singer) and, eventually, through its zeta-function trace. A little…
We propose a definition of differential operators of an associative algebra $A$ in the spirit of Hochschild cohomology. Specifically we define $D(A)$ as the zero cohomology of a certain bicomplex formed by Hom-spaces…
In a cold atom gas subject to a 2D spin-dependent optical lattice potential with hexagonal symmetry, trapped atoms undergo orbital motion around the potential minima. Such atoms are elementary quantum rotors. We develop the theory of such…
We introduce the notion of a coordinate $\mathbf{k}$-algebra scheme and the corresponding notion of a $\mathcal{B}$-operator. This class of operators includes endomorphisms and derivations of the Frobenius map, and it also generalizes the…
This article is to give an infinite dimensional analogue of a result of Choi and Effros. We say that an (not necessarily unital) operator system $T$ is \emph{dualizable} if one can find an equivalent dual matrix norm on the dual space $T^*$…
We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is…